It's easy to get the shaft out of the new bracket housing. Just depress the "dead bold" between the semi-circle bracket, twist and turn the shaft with a long-nose plier, you should be able to get it out.
I found a website that sells just the shaft for dirt cheap. It's aftermarket from overseas but it looks just like the broken one I have removed.
Search the internet for Bross BSP36
This one is $8.99
Ignition Lock Cylinder Barrel Rod For TOYOTA No:6
or this $24.99:
Ignition Lock Cylinder Barrel Rod:4528060510 For Toyota Land Cruiser,Lexus LX
NOTE: For either one of these aftermarket parts, you will be re-using the brass parts from your old shaft. So be sure note the exact position of those parts on the broken shaft to put on the new shaft. Just slide the horizontal part to one side and pull it straight up.
There is a TINY spring underneath, don't loose that!)
Although, the prices are different, look at the ID stamped on the shaft, they are the same.
My car is a 2001 LX470 with only 98,000 miles when this happened.
I ordered the cheaper one and added J&B welder to the new part to re-inforce the point where it could possibly break and after installation, I was not able to start the car. After struggling with it for a while, I was able to take it back out and realized that the tip that enters the ignition switch is wider and did not fit the ignition switch properly.
This can easily be overcome by grinding the tip to make it fit. If you are looking for a cheap way to fix your car, this the best way to go. However, my wife convinced me to go for the real Toyota part and I decided to get the part "45280-60510" for $225.00 at the local dealer (ouch!). And it really is a "beefier" shaft so it should last much longer.
Once you get the shaft out of the new housing, it's not that difficult to put in in the cylinder. Just find a
small diameter metal rod that's stiff enough for you to push the cam to one side, line up the new shaft with the notch at the tip and push it in, at the same time, pull the metal rod out. I don't think using a screw driver would work because it would be way too thick for it and the new shaft to be in the cylinder at the same time...
Here is another entire new but related issue, in case someone else runs into the same problem:
Another problem I encountered was that after everything was in place, I was able to start the car but for some reasons, there was no light in the instrument panel and I could not shift out of park! After pulling my hair out for a while, I noticed that while the car was running, if I wiggled the key a tiny bit (just a hair), the instrument light would light up and I was able to shift the transmission! Then I realized that must have something to do with the ignition switch. I removed the ignition switch at the end of the key cylinder, and with the key in "start" position, turned the switch with a screwdriver to start the car. Again the there was no light on the panel (This is something I wish I had known before so I did not have to have the car towed home!). I wiggled the switch with the screwdriver (very slight movements) and there was lights! So definitely, my ignition switch just happened to wear out along with the broken shaft.
So I got a new ignition switch (# 84450-12200), for another $105 and after installation, all was FIXED!
Hope this can help someone else with the problems. Get the aftermarket part for cheap or get the OEM part, it's your call. It's not that difficult, and you don't have to remove the entire housing. See the Youtube video posted above, it's a GREAT help!.